Plateau's Problem as a Singular Limit of Capillarity Problems. Issue 6 (11th October 2020)

• Record Type: Journal Article
• Authors: King, Darren; Maggi, Francesco; Stuvard, Salvatore
• Is Part Of: Communications on pure and applied mathematics. Volume 76:Issue 6(2023)
• Page Start: 1139
• Page End: 1207
• Publication Date: 2020-10-11
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21951
• Languages: English
• ISSNs: 0010-3640

Abstract

Abstract: Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection principle for Plateau's problem, points at physical features of soap films that are unaccessible by simply looking at minimal surfaces, and opens several challenging questions. © 2020 Wiley Periodicals LLC.